This monograph presents a view on grammaticalisation radically different from standard views centering around the cline of grammaticality. Grammar is seen as a complex sign system, and, as a consequence, grammatical change always comprises semantic change. What unites morphology, topology (word order), constructional syntax and other grammatical subsystems is their paradigmatic organisation. The traditional concept of an inflexional paradigm is generalised as the structuring principle of grammar. Grammatical change involves paradigmatic restructuring, and in the process of grammatical change morphological, topological and constructional paradigms often connect to form complex paradigms. The book introduces the concept of connecting grammaticalisation to describe the formation, restructuring and dismantling of such complex paradigms. Drawing primarily on data from Germanic, Romance and Slavic languages, the book offers both a broad general discussion of theoretical issues (part one) and three case studies (part two). As of March 2017, this e-book is freely available, thanks to the support of libraries working with Knowledge Unlatched.